Simplify; express your answer in exponential form. Assume $z\neq 0, a\neq 0$. $\dfrac{{(z^{-4})^{-5}}}{{(za^{-3})^{-4}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{-4}}$ to the exponent ${-5}$ . Now ${-4 \times -5 = 20}$ , so ${(z^{-4})^{-5} = z^{20}}$ In the denominator, we can use the distributive property of exponents. ${(za^{-3})^{-4} = (z)^{-4}(a^{-3})^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(z^{-4})^{-5}}}{{(za^{-3})^{-4}}} = \dfrac{{z^{20}}}{{z^{-4}a^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{20}}}{{z^{-4}a^{12}}} = \dfrac{{z^{20}}}{{z^{-4}}} \cdot \dfrac{{1}}{{a^{12}}} = z^{{20} - {(-4)}} \cdot a^{- {12}} = z^{24}a^{-12}$.